by Chow Ha Tak. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 96-97). / Abstract also in Chinese. / Chapter 1 --- The Laplacian on a Riemannian Manifold --- p.5 / Chapter 1.1 --- Riemannian metrics --- p.5 / Chapter 1.2 --- L2 Spaces of Functions and Forms --- p.6 / Chapter 1.3 --- The Laplacian on Functions and Forms --- p.8 / Chapter 2 --- Hodge Theory for Functions and Forms --- p.14 / Chapter 2.1 --- Analytic Preliminaries --- p.14 / Chapter 2.2 --- The Hodge Theorem for Functions --- p.20 / Chapter 2.3 --- The Hodge Theorem for Forms --- p.27 / Chapter 2.4 --- Regularity Results --- p.29 / Chapter 2.5 --- The Kernel of the Laplacian on Forms --- p.33 / Chapter 3 --- Fermion Calculus and Weitzenbock Formula --- p.36 / Chapter 3.1 --- The Levi-Civita Connection --- p.36 / Chapter 3.2 --- Fermion calculus --- p.39 / Chapter 3.3 --- "Weitzenbock Formula, Bochner Formula and Garding's Inequality" --- p.53 / Chapter 3.4 --- The Laplacian in Exponential Coordinates --- p.59 / Chapter 4 --- The Construction of the Heat Kernel --- p.63 / Chapter 4.1 --- Preliminary Results for the Heat Kernel --- p.63 / Chapter 4.2 --- Construction of the Heat Kernel --- p.66 / Chapter 4.2.1 --- Construction of the Parametrix --- p.66 / Chapter 4.2.2 --- The Heat Kernel for Functions --- p.70 / Chapter 4.2.3 --- The Heat Kernel for Forms --- p.76 / Chapter 4.3 --- The Asymptotics of the Heat Kernel --- p.77 / Chapter 5 --- The Heat Equation Approach to the Chern-Gauss- Bonnet Theorem --- p.82 / Chapter 5.1 --- The Heat Equation Approach --- p.82 / Chapter 5.2 --- Proof of the Chern-Gauss-Bonnet Theorem --- p.85 / Chapter 5.3 --- Introduction to Atiyah-Singer Index Theorem --- p.87 / Chapter 5.3.1 --- A Survey of Characteristic Forms --- p.87 / Chapter 5.3.2 --- The Hirzenbruch Signature Theorem --- p.90 / Chapter 5.3.3 --- The Atiyah-Singer Index Theorem --- p.93 / Bibliography / Notation index
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_322329 |
| Date | January 1998 |
| Contributors | Chow, Ha Tak., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, 99 leaves ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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